Bayesian isotonic density regression

• 成果类型: Article
• 署名作者: Wang, Lianming; Dunson, David B.
• 署名单位: University of South Carolina System; University of South Carolina Columbia; Duke University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr025
• 发表日期: 2011
• 页码: 537551
• 关键词: prior distributions; nonparametric-estimation; bernstein polynomials; PROBABILITY-MEASURES; monotone-functions; inference; models; mixtures; computation

摘要

Density regression models allow the conditional distribution of the response given predictors to change flexibly over the predictor space. Such models are much more flexible than nonparametric mean regression models with nonparametric residual distributions, and are well supported in many applications. A rich variety of Bayesian methods have been proposed for density regression, but it is not clear whether such priors have full support so that any true data-generating model can be accurately approximated. This article develops a new class of density regression models that incorporate stochastic-ordering constraints which are natural when a response tends to increase or decrease monotonely with a predictor. Theory is developed showing large support. Methods are developed for hypothesis testing, with posterior computation relying on a simple Gibbs sampler. Frequentist properties are illustrated in a simulation study, and an epidemiology application is considered.